In known printing units, each printing mechanism, which typically comprises a transfer cylinder, a form cylinder and an inking and damping unit, is driven by a dedicated drive motor. An impression cylinder, which can be assigned to one or more transfer cylinders, is either driven by a dedicated drive motor or is concurrently mechanically driven by a printing mechanism. Accordingly, in a printing mechanism comprising, for example, four printing mechanisms, a plurality of drive motors are used. In addition, a mechanical drive connection is not provided between the printing mechanisms in order to synchronize the printing mechanisms. If a dedicated drive motor also drives an impression cylinder, there is also no mechanical drive connection between the impression cylinder and the associated transfer cylinders. The synchronization of the printing mechanisms and the impression cylinders, each of which is driven by its own dedicated motor, is performed by the respective drive motors. As a result, the stress torques acting within the printing unit place a very high additional load on the drive motors or the loads must be relieved. For this reason, the drive motors must have a very high motor output or torque.